Metallic-covalent bonding conversion in icosahedral clusters of Al and B by small changes of the structure was demonstrated by molecular orbital calculations. According to the electron density distribution obtained using the maximum entropy method and the Rietveld method, the bonding conversion phenomenon occurs even in cluster solids such as some Al- and B-based icosahedral approximant phases (Al12Re, α-AlMnSi, α-rhombohedral boron). The multiple-shell atomic structure, the electrical and optical conductivity are compared for metal doped β-rhombohedral boron and AlLiCu or AlPdRe icosahedral quasicrystal. Photoemission and electron energy loss spectroscopy investigations for V doped β-rhombohedral have been discussed. Conclusions are the following two. It is difficult to distinguish a Hume-Rothery, i.e. structure-induced, pseudogap, and a covalent bonding, i.e. hybridization, pseudogap for materials with a highly symmetric Brillouin zone and a strong potential for valence electrons. Because hybridization is necessary not only for covalent bonds but also for metallic ones, it is better to use the covalent bonding pseudogap than the hybridization pseudogap.